zhpevx(3P) Sun Performance Library zhpevx(3P)NAMEzhpevx - compute selected eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage
SYNOPSIS
SUBROUTINE ZHPEVX(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*)
INTEGER N, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK3(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION W(*), WORK2(*)
SUBROUTINE ZHPEVX_64(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK3(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION W(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HPEVX(JOBZ, RANGE, UPLO, [N], A, VL, VU, IL, IU, ABTOL,
[NFOUND], W, Z, [LDZ], [WORK], [WORK2], [IWORK3], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX(8), DIMENSION(:) :: A, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK3, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK2
SUBROUTINE HPEVX_64(JOBZ, RANGE, UPLO, [N], A, VL, VU, IL, IU, ABTOL,
[NFOUND], W, Z, [LDZ], [WORK], [WORK2], [IWORK3], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX(8), DIMENSION(:) :: A, WORK
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK3, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK2
C INTERFACE
#include <sunperf.h>
void zhpevx(char jobz, char range, char uplo, int n, doublecomplex *a,
double vl, double vu, int il, int iu, double abtol, int
*nfound, double *w, doublecomplex *z, int ldz, int *ifail,
int *info);
void zhpevx_64(char jobz, char range, char uplo, long n, doublecomplex
*a, double vl, double vu, long il, long iu, double abtol,
long *nfound, double *w, doublecomplex *z, long ldz, long
*ifail, long *info);
PURPOSEzhpevx computes selected eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A in packed storage. Eigenvalues/vectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
ARGUMENTS
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input)
= 'A': all eigenvalues will be found;
= 'V': all eigenvalues in the half-open interval (VL,VU] will
be found; = 'I': the IL-th through IU-th eigenvalues will be
found.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array A as follows: if UPLO = 'U', A(i +
(j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i +
(j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, A is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the diag‐
onal and first subdiagonal of T overwrite the corresponding
elements of A.
VL (input)
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU. Not referenced if
RANGE = 'A' or 'I'.
VU (input)
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU. Not referenced if
RANGE = 'A' or 'I'.
IL (input)
If RANGE='I', the indices (in ascending order) of the small‐
est and largest eigenvalues to be returned. 1 <= IL <= IU <=
N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if
RANGE = 'A' or 'V'.
IU (input)
If RANGE='I', the indices (in ascending order) of the small‐
est and largest eigenvalues to be returned. 1 <= IL <= IU <=
N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if
RANGE = 'A' or 'V'.
ABTOL (input)
The absolute error tolerance for the eigenvalues. An approx‐
imate eigenvalue is accepted as converged when it is deter‐
mined to lie in an interval [a,b] of width less than or equal
to
ABTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABTOL is less than or
equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained by
reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABTOL to
2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and Kahan,
LAPACK Working Note #3.
NFOUND (output)
The total number of eigenvalues found. 0 <= NFOUND <= N. If
RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU-
IL+1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the selected eigenvalues in ascending order.
Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
If JOBZ = 'V', then if INFO = 0, the first NFOUND columns of
Z contain the orthonormal eigenvectors of the matrix A corre‐
sponding to the selected eigenvalues, with the i-th column of
Z holding the eigenvector associated with W(i). If an eigen‐
vector fails to converge, then that column of Z contains the
latest approximation to the eigenvector, and the index of the
eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is
not referenced. Note: the user must ensure that at least
max(1,NFOUND) columns are supplied in the array Z; if RANGE =
'V', the exact value of NFOUND is not known in advance and an
upper bound must be used.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
COMPLEX*16 array, dimension(2*N)
WORK2 (workspace)
DOUBLE PRECISION array, dimension(7*N)
IWORK3 (workspace)
INTEGER array, dimension(5*N)
IFAIL (output) INTEGER array, dimension (N)
If JOBZ = 'V', then if INFO = 0, the first NFOUND elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the indices
of the eigenvectors that failed to converge. If JOBZ = 'N',
then IFAIL is not referenced.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
6 Mar 2009 zhpevx(3P)
